How much of a slowdown, if any, would one see if they were to implement this as opposed to the modified Euler method? It seems that having to repeatedly compute multiple Euler steps until we reach a threshold could be rather slow.

moridin22

I think this depends on how fast your function is changing, but if each step of the loop takes constant time, then you only require logarithmic time in the (inverse) multiplicative decrease of your step size.

zsano1

So adaptive step size is used to reduce error, but is it related to make the system stable?